JournalsowrVol. 6 / No. 3DOI 10.4171/owr/2009/33

Explicit Methods in Number Theory

  • Hendrik W. Lenstra, Jr.

    University of Leiden, Netherlands
  • Don B. Zagier

    Max-Planck-Institut für Mathematik, Bonn, Germany
  • Karim Belabas

    Université de Bordeaux I, Talence, France
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These notes contain extended abstracts on the topic of explicit methods in number theory. The range of topics includes asymptotics for field extensions and class numbers, random matrices and L-functions, rational points on curves and higher-dimensional varieties, and aspects of lattice basis reduction.